The firm has beaten-off competition from Balfour Beatty Civil Engineering and John Graham Construction.
The deal is part of the Scottish Governments £257m investment in the project with the new dual carriageway due to be operational by the end of 2028.
Cabinet Secretary for Transport Fiona Hyslop said: “Our intention to award the contract for Tay Crossing to Ballinluig illustrates continued momentum in our delivery plan for dualling the A9 between Perth and Inverness.
“When work commences on this section, we will have active dualling works at both the southern and northern extents of the Programme’s corridor – a clear sign of the momentum behind our delivery plan.
“The receipt of three valid tenders during this procurement process means that we can also be confident that our investment in this A9 Dualling contract demonstrates value for money, and that the changes we have made to our contracts in recent years are making a real difference.
“We are achieving the targets we have laid out, and making steady progress across the corridor to ensure that the full route between Perth and Inverness is dualled by 2035.”